Scaling only the height of a parallelogram plane
I have a script that I think accomplishes your mission: http://web.purplefrog.com/~thoth/blender/python-cookbook/scale-parallelogram.html

import bpy
from mathutils import *


def share_vertex(e, horiz_edge):
    return e.vertices[0] in horiz_edge.vertices or e.vertices[1] in horiz_edge.vertices

def horiz_score(vector, axis):
    v2 = vector.copy()
    v2[axis]=0
    dz = abs(vector[axis])
    if dz &gt;0:
        return v2.magnitude/ dz
    else:
        return float('inf')


def most_horizontal_edge(obj, axis):

    mesh = obj.data
    global_verts = [ obj.matrix_world*v.co for v in mesh.vertices ]

    score = None
    rval = None
    for e in mesh.edges:
        v1 = global_verts[e.vertices[0]]
        v2 = global_verts[e.vertices[1]]

        s2 = horiz_score(v2-v1, axis)
        if (score is None or s2 &gt; score):
            score = s2
            rval = e

    return rval

def scale_parallelogram(obj, factor, axis):

    mesh = obj.data
    horiz_edge = most_horizontal_edge(obj, axis)

    global_verts = [ obj.matrix_world*v.co for v in mesh.vertices ]

    if True:
        other_verts = set(range(len(global_verts)))
        other_verts.difference_update(horiz_edge.vertices)
    else:
        other_verts = set()
        for e in mesh.edges:
            if share_vertex(e, horiz_edge):
                continue
            other_verts.update(e.vertices)

    #print("%r -vs- %r"%(horiz_edge.vertices[:], other_verts))

    z1 = [ global_verts[i][axis] for i in horiz_edge.vertices]
    z2 = [ global_verts[i][axis] for i in other_verts]

    z_all = [ v[axis] for v in global_verts ]
    delta_z =max(z_all)-min(z_all)
    z_change = 0.5*(1-factor)*delta_z

    delta_v = Vector([0,0,0])
    delta_v[axis] = z_change

    #print(global_verts[0])
    mwi = obj.matrix_world.inverted()
    if (min(z1) &lt; min(z2)):
        delta_v = -delta_v

    for i in horiz_edge.vertices:
        mesh.vertices[i].co = mwi * (global_verts[i] - delta_v)
    for i in other_verts:
        mesh.vertices[i].co = mwi * (global_verts[i] + delta_v)

    #print(mesh.vertices[0].co)

    mesh.update()

#
#

x_axis=0
y_axis=1
z_axis=2

for obj in bpy.context.selected_objects:
    scale_parallelogram(obj, 0.5, z_axis)